U.S. Pat. No. 6,625,907 (Murray et al.) entitled “Method and apparatus for dredging and transporting dredged solids” describes a method and apparatus for dredging bodies of water. The method uses a barge or other suitable motorized self-contained vessel. The vessel illustrated and used as an example in the Murray et al. patent reference is stated to be one hundred and eighty feet long and fifty four feet wide. One or more dredge shoes are suspended by a first set of cables from booms. The first cables maintain a roughly vertical orientation, subject to some angular variation. There are also second set of cables extending from a riser assembly to the one or more dredge shoes. The riser has a horizontal section that is lowered into the water and positioned proximate to a bottom of a body of water to be dredged so that the cables are maintained in a roughly horizontal orientation. A finite control system is described for repositioning the vessel during dredging using cables and winches and aided by a global positioning system. While the Murray et al. method and apparatus has merit, it is not suitable for use in settling ponds and other small bodies of water. There will now be described a method and associate apparatus that has been developed expressly for the purpose of dredging settling ponds and other small bodies of water.